Residual stresses and their effects on deformation
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INTRODUCTION
M E T A L - m a t r i x composites (MMC) have received substantial attention as light weight, but strong materials. Proven and potential applications in aerospace and automotive industries have been discussed extensively. I~l Particle-reinforced composites are being considered in several engine applications, such as connecting rods and cylinder liners and as drive shafts and disk brake rotors. 12~These potential applications have indicated a need for fundamental understanding of the thermal and mechanical properties of the materials. In the fabrication and subsequent heat treatment of MMCs, the material may be in a stress-free state at an elevated temperature, but it will develop rather large stresses upon cooling to room temperature. The change in temperature is several hundred K. The coefficient of thermal expansion (CTE) of the matrix (typically AI) is considerably larger than that of the ceramic inclusion (SiC or TIC), so compressive stresses develop in the particle (which are assumed to be roughly spherical). Stresses of either sign, but similar magnitude, develop in the matrix. Since the matrix residual stresses can exceed the yield stress of the metal, plastic flow can occur. A number of mechanical properties of the composite (elastic moduli, yield stress, creep rate, and fatigue lifetime) are expected to be modified by the residual stresses and plastic regions. It is now possible to measure residual strains in materials by neutron diffraction, 13'41 which, like X-ray diffraction, measures lattice constants from which local elastic strains can be calculated. Such experiments have been carried out on SiC/AI and TiC/A1 recently iS1 and the data are currently being analyzed to determine the residual stresses. The purpose of the present work is to develop methods of calculating the residual stresses and strains from a L.C. DAVIS, Principal Research Scientist, and J.E. ALLISON, Staff Scientist, are with the Research Laboratory, Ford Motor Company, MD 3028SRL, Dearborn, MI 48121-2053. Manuscript submitted April 2, 1993. METALLURGICAL TRANSACTIONS A
knowledge of the properties of the constituents. The calculations rely heavily on the technique of finite element analysis (FEA). The calculated or theoretical results can then be compared to the experiment and used in the interpretation of data. Work on residual stresses reported thus far has focused more on whisker reinforcements 16'7] than on particle systems. Since one of the systems studied by neutron diffraction involves TiC particles that are nearly spherical, the emphasis here will be on spherical particles and interactions of their stress fields. Of the authors who considered spherical inclusions, their analyses were limited to axisymmetric (2D) cell models t8'91 or to isolated particles, t")i Neither approach is entirely satisfactory. The influence of thermally induced residual stresses on subsequent deformation has been neglected in previous investigations with the notable exception of Reference 8. Previous comparisons of theory to experime
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